I am trying to measure the output of a L7805ACT voltage regulator (datasheet) with a multimeter, without any additional parts (no caps, etc, just the regulator). I'm using a regulated wall adapter power supply with settable output (5-12VDC). The adapter's connector can be inversed so + becomes -, but I paid attention to connect it the right way.

With the first regulator I tried, the multimeter displays the input voltage and the regulator quickly heats. No voltage drop whatsoever.

At first I thought 12V input is too much, 7V have to be dissipated as heat and that the overheating is normal, so I set the input to 7.5V, but the results were the same.

Changed the wall adapter, same thing. Measured the adapter's output power with the same multimeter, 7.5V exactly as set.

Tried with another regulator, 7.5V input, and now the measured output voltage starts from about 7V and rapidly drops to 0 (didn't really waited to get to 0, don't want to see the regulator burning).

Although the multimeter shouldn't be the problem, as even without connecting it the regulator still heats, I thought to change the multimeter batteries. Low battery indicator was showing on the multimeter, although the batteries were only half discharged. I changed them anyway. Same result.

So what am I doing wrong? Does the regulator need a load on the output, like a resistor? This might sound stupid, but does the multimeter draw too much current from the regulator?